Scientific Notation Calculator
Convert a decimal to a × 10^n form, or multiply a coefficient by a power of ten to get the decimal back, with the place-value steps used in class.
- The decimal point must move 4 places left so the coefficient is at least 1 and less than 10.
- Coefficient = 45000 / 10^4 = 4.5.
- Therefore 45000 = 4.5 × 10^4.
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How to Use the Scientific Notation Calculator
Choose a direction. Decimal to scientific takes one number and writes it as a coefficient times a power of ten. Scientific to decimal takes a coefficient and an integer exponent and multiplies them.
- Select Decimal to scientific or Scientific to decimal.
- Enter the decimal, or the coefficient and exponent.
- Select Convert. Reset restores the default example for the current direction.
If the coefficient you type is outside 1 ≤ |a| < 10, the decimal is still computed, and the normalized scientific form is shown beside it. This page does not do engineering notation (powers that are multiples of 3) or significant-figure rounding.
The a × 10^n Form
Ten to an integer power is a 1 followed by |e| zeros, or a 1 in the |e|-th decimal place when e is negative. Multiplying by 10^e slides the decimal point e places left or right. Choosing a so that only one non-zero digit sits to the left of the decimal makes every number (except 0) look the same: a short coefficient and a counting exponent.
Zero is the exception. There is no way to write 0 with a coefficient in [1, 10), so the calculator reports 0 × 10^0.
Scientific Notation Examples
A large whole number
45000 has the decimal point after the last zero. Moving it four places left produces 4.5000, which is 4.5. The move was left, so the exponent is +4, and 45000 = 4.5 × 10^4.
A small decimal
0.0072 needs the point moved three places right to become 7.2. Rightward moves make a negative exponent: 0.0072 = 7.2 × 10^−3.
The number 1
1 is already between 1 and 10, so no move is required: 1 = 1 × 10^0. This is the degenerate case that checks the exponent-zero rule.
A negative
−45000 uses the same places as 45000. The minus sign stays on the coefficient: −4.5 × 10^4. The exponent is not negative just because the number is negative.
Back to a decimal
4.5 × 10^4 means 4.5 followed by sliding the point four places right, which is 45000. 7.2 × 10^−3 slides three places left: 0.0072.
Why the Exponent Has a Sign
The sign of the exponent is about size, not about whether the original number is positive or negative. Positive exponents are numbers at least 10 in absolute value. Negative exponents are numbers between −1 and 1, excluding 0. The sign of the number itself lives on the coefficient.
Prime factorization writes an integer as a product of primes. Scientific notation writes any real number (in range) as a product of a short decimal and a power of ten. They answer different questions: which primes, versus how many place values.
Common Scientific Notation Mistakes
Leaving more than one digit before the decimal
45 × 10^3 equals 45000, but it is not standard scientific notation. Move one more place: 4.5 × 10^4.
Giving the exponent the sign of the number
−45000 is −4.5 × 10^4, not 4.5 × 10^−4. 4.5 × 10^−4 is 0.00045.
Counting zeros instead of place moves
45000 has four zeros in the usual writing, and the move happens to be 4, but 40500 is 4.05 × 10^4 — still four places, even though there are only two zeros at the end.
Writing 10^4 as 10 × 4
The 4 is an exponent, not a factor. 10^4 = 10000, and 10 × 4 = 40.
Forgetting that 10^0 is 1
Any non-zero number to the power 0 is 1, so 7 × 10^0 = 7.
Scientific Notation FAQs
How do you convert a number to scientific notation?
Move the decimal point until the coefficient has absolute value at least 1 and less than 10. The exponent is the number of places moved: positive for a left move, negative for a right move.
What is 45000 in scientific notation?
45000 = 4.5 × 10^4.
What is 0.0072 in scientific notation?
0.0072 = 7.2 × 10^−3.
How do you convert scientific notation to a decimal?
Multiply the coefficient by 10 to the exponent: slide the decimal point that many places right if the exponent is positive, left if it is negative.
Is 45 × 10^3 scientific notation?
It equals 45000, but standard form requires 1 ≤ |a| < 10, so the standard writing is 4.5 × 10^4.
Are my numbers sent to a server?
No. The calculation runs locally in your browser.
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Reviewed by Prof. Dr. Khalil Mudassar (PhD) · Last updated: [mc_modified_date]
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Disclaimer
This calculator is for general educational use. It does not apply significant-figure rules or engineering notation. Review important results before relying on them in laboratory or professional work.